I looked. 2016 and 2017 when Big 12 only got one team in, the runner up both years (Ok St & TCU) was the #13 team and first team out. If we stay in the top 12 (even with a CCG loss) we should be good. Which means it has to be a good game and close loss, but hey, let's just win and remove all doubt.
Oklahoma State was #12 in 2016. They didn't get in (and neither did #10 Colorado) because there were automatic spots taken by lower-ranked teams (#14 Auburn as the second SEC team and #15 Western Michigan as the G5 rep).
In 2017, the bigger hurdle was that the Sugar was a semi so there was no soft landing spot for a second Big 12 team -- unlike 2015, when #16 OSU got the second spot over #11 TCU due to the head-to-head win.
That's why it's important that there are as few automatic spots taken by teams outside the top 12. This year, #11 may be the cutoff thanks to the Pac-12.